System and method for estimating at least one characteristic of a motor vehicle suspension

ABSTRACT

The invention relates to a system for estimating at least one characteristic of a motor vehicle suspension, whereby said suspension or each suspension connects a motor vehicle wheel to the body shell thereof. The inventive system comprises means ( 12, 14 ) for acquiring vertical accelerations experienced by the wheel and body shell in a reference system of the vehicle and means ( 26 ) for calculating the at least one characteristic of the suspension as a function of the vertical accelerations acquired from the wheel and the body shell.

The present invention concerns a method and a system for estimating atleast one characteristic of a suspension connecting a motor vehiclewheel to the body of this vehicle.

The characteristics of a suspension connecting a motor vehicle wheel tothe body of this vehicle are magnitudes that influence the directionalstability of the vehicle and the effectiveness of wheel anti-blockingand vehicle trajectory control systems.

Systems for estimating certain characteristics of the suspension areknown. Typically, these systems comprise sensors that measure directlythe clearance and means for estimating the clearance variation speed,the vehicle mass, and the coefficient of stiffness and dampingcoefficient of the suspension.

Such systems use maps to estimate these characteristics. These maps aredetermined at the factory for a group of vehicles of the same category.

In practice, these systems have shown little robustness to variations inthe operation of the suspension, such as the worn state of the shockabsorbers. In addition, the precision of these systems can beunsatisfactory.

The objective of the present invention is to remedy the above-mentionedproblem by proposing a system that estimates characteristics of thesuspension with precision and robustness regarding the operating stateof this suspension.

To this effect, an object of the invention is a system for estimating atleast one characteristic of at least one motor vehicle suspension, theor each suspension connecting a motor vehicle wheel to the body of thisvehicle, characterized in that it comprises means for acquiring thevertical accelerations of the wheel and of the body in a referential ofthe vehicle and means for calculating the at least one characteristic ofthe suspension as a function of the acquired vertical accelerations ofthe wheel and of the body.

According to particular embodiments, the invention includes one or moreof the following characteristics:

-   -   each of the at least one characteristic is selected from the        group consisting of the clearance of the suspension, the        clearance variation speed of the suspension, the coefficient of        stiffness of the suspension, the damping coefficient of the        suspension, the spring force of the suspension, and the damping        force of the suspension;    -   the means for calculating the at least one characteristic are        adapted to calculate this at least one characteristic based on a        mono-wheel mechanical model of the wheel connected to the body        thereof by means of the suspension;    -   the calculation means comprise means forming Kalman estimator        adapted to estimate the at least one characteristic from the        mono-wheel mechanical model;    -   the means forming Kalman estimator are adapted to implement an        extended Kalman estimator of the state vector

${\begin{pmatrix}z_{1} & z_{2} & z_{3} & z_{4}\end{pmatrix}^{T} = \begin{pmatrix}{deb} & {Vdeb} & \frac{K_{c}}{m_{c}} & \frac{R_{c}}{m_{c}}\end{pmatrix}^{T}},$

where z_(i), i−1, . . . , 4, is a state variable, deb is the clearance,Vdeb is the clearance variation speed, m_(c) is the mass of the vehiclebody adjusted to the wheel, K_(c) is the coefficient of stiffness of thesuspension, and R_(c) is the damping coefficient of the suspension;

-   -   the means forming Kalman estimator are adapted to estimate the        state vector (x₁×₂)^(T)=(deb Vdeb)^(T), where deb is the        clearance of the suspension and Vdeb is the clearance variation        speed of the suspension;    -   it further comprises means for acquiring longitudinal and        lateral accelerations of the body, and in that the means for        calculating the at least one characteristic are adapted to        calculate this at least one characteristic based on a mono-wheel        mechanical model of the wheel taking into account load transfers        in the area of the wheel;    -   the means for acquiring the vertical accelerations of the wheel        and of the body comprise an accelerometer arranged in the body        in vertical alignment with the wheel;    -   the vehicle is equipped with four suspensions connecting four        wheels to the body of this vehicle, and it comprises, associated        with each group composed of a suspension connecting a wheel to        the body of the vehicle, accelerometers to measure the vertical        accelerations of the wheel and of the body.

Another object of the invention is a method of estimating at least onecharacteristic of a motor vehicle suspension, the or each suspensionconnecting a motor vehicle wheel to the body of this vehicle,characterized in that it comprises a step of acquiring the verticalaccelerations of the wheel and of the body in a referential of thevehicle, and a step of calculating the at least one characteristic ofthe suspension as a function of the acquired vertical accelerations ofthe wheel and of the body.

The invention will be better understood by reading the followingdescription, which is given by way of example only, in reference to theannexed drawings in which:

FIG. 1 is a mechanical model of a motor vehicle wheel connected to thebody of this vehicle by a suspension;

FIG. 2 is a schematic view of a system according to the invention;

FIG. 3 is a flow chart of the method implemented by the system of FIG.2;

FIG. 4 is a graph on which are traced, as a function of time, theclearance estimated by the system of FIG. 2 and the clearance estimatedby a sensor;

FIG. 5 is a graph on which are traced, as a function of time, theclearance variation speed estimated by the system of FIG. 2 and thederivative of the clearance measured by a sensor; and

FIG. 6 is a graph on which are traced, as a function of time, theclearance estimated by the system of FIG. 2, taking into account theload transfer to the wheel of the vehicle and the clearance measured bya sensor.

FIG. 1 illustrates a mono-wheel mechanical model of a wheel R of a motorvehicle having four wheels, connected to the body C of this vehicle bymeans of a suspension Su, the wheel R being in contact with the groundSo.

In this model, the body C has a mass at the wheel m_(c). The suspensionSu is modeled by a spring having a coefficient of stiffness K_(c) inparallel with a shock absorber having a damping coefficient R_(c).Lastly, the wheel R has a mass m_(r) and the tire of this wheel ismodeled by a spring having a coefficient of stiffness K_(r).

The distance between the wheel R and the body C is called clearance.

Using the fundamental principle of dynamics, it can be shown that themono-wheel mechanical model of FIG. 1 satisfies the following equations:

$\begin{matrix}\left\{ {{\begin{matrix}{{\overset{.}{z}(t)} = {\begin{bmatrix}{z_{2}(t)} \\{{{- {z_{3}(t)}}{z_{1}(t)}} - {{z_{4}(t)}{z_{2}(t)}}} \\0 \\0\end{bmatrix} + {\begin{bmatrix}0 \\1 \\0 \\0\end{bmatrix}{A_{r}(t)}}}} \\{{A_{c}(t)} = \left\lbrack {{{z_{3}(t)}{z_{1}(t)}} + {{z_{4}(t)}{z_{2}(t)}}} \right\rbrack}\end{matrix}{with}{z(t)}} = {\begin{bmatrix}{{deb}(t)} \\{{Vdeb}(t)} \\{\frac{K_{c}}{m_{c}}(t)} \\{\frac{R_{c}}{m_{c}}(t)}\end{bmatrix} = \begin{bmatrix}{z_{1}(t)} \\{z_{2}(t)} \\{z_{3}(t)} \\{z_{4}(t)}\end{bmatrix}}} \right. & (1)\end{matrix}$

where t is time, deb is the clearance, Vdeb is the clearance variationspeed, and A_(r) and A_(c) are vertical accelerations of the wheel andof the body, respectively, i.e., the accelerations of the wheels and ofthe body along the axis Oz of a referential Ref of the motor vehicle.

The above model represents well the transmission of the solicitations bythe ground through the suspension up to the body, but it does not takeload transfers into account. That is, the vertical load supported by thesuspension varies when the vehicle is turning, braking, andaccelerating. For example, when braking, the front suspension supportsan additional vertical load and the rear suspension is relieved of thissame load. This is called a load transfer from the rear to the frontduring braking, and this load transfer generates an additional forcethat applies to the body and triggers a low frequency movement of thebody.

The force due to the load transfers is defined as a function of thelateral and longitudinal accelerations of the body of the vehicleaccording to the equation Transfert=αA_(longi)+βA_(lat), where α and βare predetermined load transfer coefficients, A_(longi) is thelongitudinal acceleration of the body, and A_(lat) is the lateralacceleration of the body.

To take into account the solicitations in the area of the ground and thesolicitations in the area of the body due to the load transfers whenturning, braking or accelerating, the state representation according tothe equations (1) are redefined as follows:

$\begin{matrix}\left\{ \begin{matrix}{{\overset{.}{z}(t)} = {\begin{bmatrix}{z_{2}(t)} \\{{{- {z_{3}(t)}}{z_{1}(t)}} - {{z_{4}(t)}{z_{2}(t)}}} \\0 \\0\end{bmatrix} + {\begin{bmatrix}0 & 0 & 0 \\1 & {- \alpha} & {- \beta} \\0 & 0 & 0 \\0 & 0 & 0\end{bmatrix}\begin{pmatrix}{A_{r}(t)} \\{A_{longi}(t)} \\{A_{lat}(t)}\end{pmatrix}}}} \\{{A_{c}(t)} = {\left\lbrack {{{z_{3}(t)}{z_{1}(t)}} + {{z_{4}(t)}{z_{2}(t)}}} \right\rbrack + {\left\lbrack {0\mspace{14mu} \alpha \mspace{14mu} \beta} \right\rbrack \begin{pmatrix}{A_{r}(t)} \\{A_{longi}(t)} \\{A_{lat}(t)}\end{pmatrix}}}}\end{matrix} \right. & (2)\end{matrix}$

The coefficients α and β are determined according to the equations:

${- \alpha} = {{{- \frac{2h}{E - a}}\mspace{14mu} {and}\mspace{14mu} \beta} = \frac{2h}{v}}$

for the left front wheel of the vehicle,

${- \alpha} = {{{- \frac{2h}{E - a}}\mspace{14mu} {and}\mspace{14mu} \beta} = {- \frac{2h}{v}}}$

for the right front wheel of the vehicle,

${- \alpha} = {{\frac{2h}{a}\mspace{14mu} {and}\mspace{14mu} \beta} = {- \frac{2h}{v}}}$

for the right rear wheel of the vehicle,

${- \alpha} = {{\frac{2h}{a}\mspace{14mu} {and}\mspace{14mu} \beta} = \frac{2h}{v}}$

for the left front wheel of the vehicle,

where E is the wheel base of the vehicle, v is the wheel track of thevehicle, h is the height of the center of gravity of the vehicle, and ais the position of the center of gravity with respect to the middle ofthe front axle of the vehicle.

We will now describe, with reference to FIG. 2, first embodiment of asystem for estimating the characteristics of a motor vehicle suspensionconnecting a wheel to the body of this vehicle, based on the mono-wheelmodel of state representation according to the equations (1), and moreparticularly on a discretization of the state representation.

This system is designated by the general reference 10 and includes anmono-axis accelerometer 12 arranged in the area of the center of thewheel and measuring the vertical acceleration A_(r) of this wheel.

The system 10 also comprises a mono-axis accelerometer 14 arranged inthe body of the vehicle in vertical alignment with the wheel andmeasuring the vertical acceleration A_(c) of the body.

Each of the accelerometers 12, 14 comprises means 16, 18 formingemitting antenna for supplying an electromagnetic signal representingthe vertical acceleration A_(r), A_(c) that it measures.

Means 20 forming receiving antenna are provided in the system 10 toreceive the signals emitted by the accelerometers 12, 14 and to extractfrom these signals the accelerations A_(r), A_(c) measured by theseaccelerometers.

The means 20 are connected to a low-pass filter 22 adapted to processthe accelerations A_(r), A_(c) of the wheel and of the body supplied bythe means 20 by filtering out the high frequency noises using thelow-pass filter. The filtering operation on the accelerations is carriedout, for example, in a frequency range substantially equal to the range[0; 50] Hz.

As a variant, the low-pass filter 22 is omitted.

The low-pass filter 22 is further connected to an analog/digitalconverter 24, for example, a zero-order sample and hold circuit, adaptedto digitalize the filtered accelerations with a predetermined samplingperiod T, for example, comprised between about 50 Hz and 1000 Hz, andthus, to supply as output digital accelerations A_(r)(k), A_(c)(k) ofthe wheel and of the body, where k represents the k^(th) samplinginstant.

The sampling circuit 24 is connected to a computing unit 26 thatestimates the state vector z as a function of the digital accelerationsA_(r)(k), A_(c)(k) from the state representation according to theequations (1) discretized according to the period T.

More particularly, the computing unit 26 comprises a module 28implementing an extended Kalman estimator of the state vector zaccording to the equations:

$\begin{matrix}{{{\hat{z}}^{-}(k)} = {{\begin{pmatrix}1 & T & 0 & 0 \\{{- {{\hat{z}}_{3}\left( {k - 1} \right)}}*T} & {1 - {{{\hat{z}}_{4}\left( {k - 1} \right)}*T}} & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{pmatrix}{\hat{z}\left( {k - 1} \right)}} + {\begin{pmatrix}0 \\T \\0 \\0\end{pmatrix}{A_{r}\left( {k - 1} \right)}}}} & (3) \\{{A(k)} = \begin{pmatrix}1 & T & 0 & 0 \\{{- {{\hat{z}}_{3}\left( {k - 1} \right)}}*T} & {1 - {{{\hat{z}}_{4}\left( {k - 1} \right)}*T}} & {{- {{\hat{z}}_{1}\left( {k - 1} \right)}}*T} & {{- {{\hat{z}}_{2}\left( {k - 1} \right)}}*T} \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{pmatrix}} & (4) \\{{B(k)} = \begin{pmatrix}0 & T & 0 & 0\end{pmatrix}} & (5) \\{{P^{-}(k)} = {{{A(k)} \cdot {P\left( {k - 1} \right)} \cdot {A^{T}(k)}} + {{B(k)} \cdot {Q(k)} \cdot {B^{T}(k)}} + {Q_{0}(k)}}} & (6) \\{{h\left( {{\hat{z}}^{-}(k)} \right)} = {\left( {{{\hat{z}}_{3}(k)}\mspace{14mu} {{\hat{z}}_{4}(k)}\mspace{14mu} 0\mspace{14mu} 0} \right){{\hat{z}}^{-}(k)}}} & (7) \\{{C(k)} = \begin{pmatrix}{{\hat{z}}_{3}^{-}(k)} & {{\hat{z}}_{4}^{-}(k)} & {{\hat{z}}_{1}^{-}(k)} & {{\hat{z}}_{2}^{-}(k)}\end{pmatrix}} & (8) \\{{K(k)} = {{P^{-}(k)} \cdot {C^{T}(k)} \cdot \left( {{{C(k)} \cdot {P^{-}(k)} \cdot {C^{T}(k)}} + {R(k)}} \right)^{- 1}}} & (9) \\{{P(k)} = {\left( {I - {{K(k)} \cdot {C(k)}}} \right){P^{-}(k)}}} & (10) \\{{\hat{z}(k)} = {{{\hat{z}}^{-}(k)} + {{K(k)} \cdot \left( {{A_{c}(k)} - {h\left( {{\hat{z}}^{-}(k)} \right)}} \right)}}} & (11)\end{matrix}$

where {circumflex over (z)}⁻(k)=({circumflex over (z)}(k) {circumflexover (z)}₂ ⁻(k) {circumflex over (z)}₃ ⁻(k) {circumflex over (z)}₄⁻(k))^(T) is the prediction of the state vector z at instant k,{circumflex over (z)}(k)=({circumflex over (z)}₁(k) {circumflex over(z)}₂(k) {circumflex over (z)}₃(k) {circumflex over (z)}z₄ (k))^(T) isthe estimation of the state vector z at instant k, P (k) is theprediction of the covariance of the estimation error at instant k, P(k)is the estimation of the error covariance at instant k, K(k) is theKalman gain at instant k, Q₀ is the covariance of the state noise, Q isthe covariance of the measurement noise of the vertical acceleration ofthe wheel, and R is the covariance of the measurement noise of thevertical acceleration of the body.

The covariances Q and R are supplied, for example, by the manufacturersof the accelerometers 12, 14, or they are determined in a previousstatistical study, also performed to determine the covariance Q₀.

The Kalman estimator begins, for example, by the prediction of thevector z during startup of the vehicle by selecting, for the initialvalue of the state vector z, a value of the clearance of the vehicle atrest memorized in the module 28 and determined during the previousstudy, or a clearance value of zero, a clearance variation speed ofzero, the last estimations of the coefficient of stiffness and of thedamping coefficient of the suspension determined during the lastimplementation of the Kalman estimator, or the values of thesecoefficients given by the manufacturer of the suspension if the Kalmanestimator is implemented for the first time.

The unit 26 also comprises a computing module 30 connected to theestimation module 28 and adapted to calculate at each sampling instantk:

-   -   an estimation {circumflex over (K)}_(c)(k) of the coefficient of        stiffness of the suspension by multiplying the estimation

${{\hat{z}}_{3}(k)} = {\frac{{\hat{K}}_{c}}{m_{c}}(k)}$

of the third variable of the state vector z by the mass m_(c) of thebody adjusted to the wheel;

-   -   an estimation {circumflex over (R)}_(c)(k) of the damping        coefficient of the suspension by multiplying the estimation

${{\hat{z}}_{4}(k)} = \frac{{\hat{R}}_{c}}{m_{c}}$

of the fourth variable of the state vector z by the mass m_(c) of thebody adjusted to the wheel;

-   -   an estimation {circumflex over (F)}_(spring) (k) of the spring        force of the suspension by multiplying the estimation        {circumflex over (z)}₁(k)=dêb(k) of the first variable of the        state vector z by the estimation {circumflex over (K)}_(c)(k) of        the coefficient of stiffness of the suspension; and    -   an estimation {circumflex over (F)}_(damp)(k) of the damping        force of the suspension by multiplying the estimation        {circumflex over (z)}₁(k)=V{circumflex over (d)}eb(k) of the        second variable of the state vector z by the estimation        {circumflex over (R)}_(c)(k) of the damping coefficient of the        suspension.

Lastly, the unit 26 is connected to a control and diagnostic unit 32adapted to control the operation of the vehicle and to diagnose theoperating state of the suspension as a function of the estimations{circumflex over (z)}₁(k)=dêb(k), {circumflex over (z)}₂(k)=V{circumflexover (d)}eb(k), {circumflex over (K)}_(c)(k), {circumflex over(R)}_(c)(k), {circumflex over (F)}_(spring)(k) and {circumflex over(F)}_(damp)(k) calculated by the estimation and computing modules 28,30.

We will now describe, still in reference to FIG. 2, a second embodimentof the system according to the invention based on the mono-wheel modelof state representation according to equations (2), and moreparticularly a discretization of this representation according to thesampling period T.

This embodiment is structurally analogous to the first embodiment whichis described above. In the second embodiment, the accelerometer 14 is atri-axis accelerometer measuring the vertical A_(c), longitudinalA_(longi), and lateral A_(lat) accelerations of the body, i.e.,measuring the accelerations of the body according to axes OZ, OY, and OYof the referential Ref of the vehicle.

The measurements of these accelerations are emitted by the means 16, 18forming emitting antenna of the accelerometers 12 and 14, received bythe means 20 forming receiving antenna, then filtered and sampled by thefilter 22 and sampler 24. The digital accelerations A_(c)(k),A_(longi)(i), A_(lat)(k) of the body, and the digital acceleratorA_(r)(k) of the wheel are then supplied to the estimation module 28.

The module 28 implements, as a function of these values, an extendedKalman estimator of the state vector z analogous to that describedabove, in which the equations (3), (4), (5), and (7) are replaced by thefollowing equations (12), (13), (14), and (15), respectively:

$\begin{matrix}{{z^{-}(k)} = {{\begin{bmatrix}1 & T & 0 & 0 \\{{- {{\hat{z}}_{3}\left( {k - 1} \right)}}*T} & {1 - {{{\hat{z}}_{4}\left( {k - 1} \right)}*T}} & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}{\hat{z}\left( {k - 1} \right)}} + {\begin{bmatrix}0 & 0 & 0 \\T & {{- \alpha}\; T} & {{- \beta}\; T} \\0 & 0 & 0 \\0 & 0 & 0\end{bmatrix}\begin{pmatrix}{A_{r}(k)} \\{A_{{longi}\;}(k)} \\{A_{lat}(k)}\end{pmatrix}}}} & (12) \\{{A( k)} = \mspace{661mu} \left\lbrack \begin{matrix}1 & T & 0 & 0 \\{{- {{\hat{z}}_{3}\left( {k - 1} \right)}}*T} & {1 - {{{\hat{z}}_{4}\left( {k - 1} \right)}*T}} & {{- {{\hat{z}}_{1}\left( {k - 1} \right)}}*T} & {{- {{\hat{z}}_{2}\left( {k - 1} \right)}}*T} \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{matrix} \right\rbrack} & (13) \\{{B(k)} = \begin{bmatrix}0 & 0 & 0 \\T & {{- \alpha}\; T} & {{- \beta}\; T} \\0 & 0 & 0 \\0 & 0 & 0\end{bmatrix}} & (14) \\{{h\left( {{\hat{z}}^{-}(k)} \right)} = {{\left\lbrack {{{\hat{z}}_{3}(k)}\mspace{14mu} {{\hat{z}}_{4}(k)}\mspace{14mu} 0\mspace{14mu} 0} \right\rbrack {{\hat{z}}^{-}(k)}} + {\left\lbrack {0\mspace{14mu} \alpha \mspace{14mu} \beta} \right\rbrack \begin{pmatrix}{A_{r}(k)} \\{A_{{longi}\;}(k)} \\{A_{lat}(k)}\end{pmatrix}}}} & (15)\end{matrix}$

Lastly, the module 30 calculates the estimations {circumflex over(K)}_(c)(k), {circumflex over (R)}_(c)(k), {circumflex over(F)}_(spring)(k) and {circumflex over (F)}_(damp) (k) in theabove-described manner.

FIG. 4 is a flow chart of the method according to the inventionimplemented by the system of FIG. 2.

In a first initialization step 40, the various parameters required forthe estimation of the state vector z by extended Kalman estimation,i.e., the covariances Q, R, Q₀ and the initial value of the state vectorz are determined.

In a subsequent step 42, the digital measurements A_(r)(k) and A_(c)(k),or the digital measurements A_(r)(k), A_(c)(k), A_(longi)(k),A_(lat)(k), and A_(c)(k) at instant k of the accelerations of the wheeland of the body are determined by filtering and sampling. At 44, aprediction {circumflex over (z)}⁻(k) of the state vector z iscalculated, then, at 46, an estimation {circumflex over (z)}⁻(k) of thestate vector z is calculated.

In a subsequent step 48, the estimations {circumflex over (K)}_(c)(k),{circumflex over (R)}_(c)(k), {circumflex over (F)}_(spring)(k) and{circumflex over (F)}_(damp)(k) are calculated as a function of theestimation {circumflex over (z)}(k) and of the mass m_(c) of the bodyadjusted to the wheel.

A step 50 of controlling the operation of the vehicle and of diagnosingthe operating state of the suspension as a function of the estimations{circumflex over (z)}₁(k)=dêb(k), {circumflex over (z)}₂(k)=V{circumflexover (d)}eb(k), {circumflex over (K)}_(c)(k), {circumflex over(R)}_(c)(k), {circumflex over (F)}_(spring)(k) and {circumflex over(F)}_(damp)(k) is then triggered. Step 50 then loops back to step 42 fora new computing cycle.

FIG. 4 is a graph on which have been traced, as a function of time, theclearance estimated by the first embodiment of the system of FIG. 2 andthe clearance measured by a sensor. FIG. 5 is a graph on which have beentraced, as a function of time, the clearance variation speed estimatedby the first embodiment of the system shown on FIG. 2 and the derivativeof the clearance measured by a sensor.

As can be observed, the first embodiment of the system according to theinvention estimates with precision the variations of the clearance andof the clearance variation speed of the suspension, which are mainlycaused by the transmission of the solicitations by the ground to thebody of the vehicle through the suspension.

FIG. 6 is a graph on which have been traced, as a function of time, theclearance estimated by the second embodiment of the system shown on FIG.2, taking into account the load transfer to the wheel of the vehicle andthe clearance measured by a sensor.

As can be observed, this second embodiment of the system according tothe invention estimates with precision the variations of the clearanceand of the clearance variation speed of the suspension caused by thetransmission of the solicitations by the ground. This second embodimentalso estimates with precision the slow dynamics solicitations. That is,taking into account the load transfers at the wheel makes it possible toestimate the very low frequency movements of the body of the vehiclecaused, for example, when the vehicle is braking, accelerating, orturning.

A system for estimating characteristics of a motor vehicle suspensionbased on a non-linear state representation mechanical model has beendescribed.

As a variant, the system is adapted to estimate the clearance and theclearance variation speed of the suspension by implementing a Kalmanestimator based on a discretization of one or the other of the linearstate representations according to the following equations (16) and(17), the coefficient of stiffness K_(c), the damping coefficient R_(c),and the mass m_(c) of the body adjusted to the wheel being consideredconstant and of known values:

$\begin{matrix}\left\{ {\begin{matrix}{{\overset{.}{x}(t)} = {{\begin{bmatrix}0 & 1 \\{- \frac{K_{c}}{m_{c}}} & {- \frac{R_{c}}{m_{c}}}\end{bmatrix}{x(t)}} + {\begin{bmatrix}0 \\1\end{bmatrix}{u(t)}}}} \\{{y(t)} = {\left\lbrack {\frac{K_{c}}{m_{c}}\mspace{14mu} \frac{R_{c}}{m_{c}}} \right\rbrack {x(t)}}}\end{matrix}\mspace{14mu} {with}\mspace{14mu} \left\{ \begin{matrix}{{x(t)} = \begin{bmatrix}{{deb}(t)} \\{{Vdeb}(t)}\end{bmatrix}} \\{{u(t)} = {A_{r}(t)}} \\{y = {A_{c}(t)}}\end{matrix} \right.} \right. & (16) \\\left\{ {\begin{matrix}{{\overset{.}{x}(t)} = {{\begin{bmatrix}0 & 1 \\{- \frac{K_{c}}{m_{c}}} & {- \frac{R_{c}}{m_{c}}}\end{bmatrix}{x(t)}} + {\begin{bmatrix}0 & 0 & 0 \\1 & {- \alpha} & {- \beta}\end{bmatrix}{u(t)}}}} \\{{y(t)} = {{\left\lbrack {\frac{K_{c}}{m_{c}}\mspace{14mu} \frac{R_{c}}{m_{c}}} \right\rbrack {x(t)}} + {\left\lbrack {0\mspace{14mu} \alpha \mspace{14mu} \beta} \right\rbrack {u(t)}}}}\end{matrix} {with}\; \left\{ \begin{matrix}{{x(t)} = \begin{bmatrix}{{deb}(t)} \\{{Vdeb}(t)}\end{bmatrix}} \\{{u(t)} = \begin{bmatrix}{A_{r}(t)} \\{A_{longi}(t)} \\{A_{lat}(t)}\end{bmatrix}} \\{{y(t)} = {A_{c}(t)}}\end{matrix} \right.} \right. & (17)\end{matrix}$

Similarly, a system for estimating characteristics of a motor vehiclesuspension has been described.

As a variant, this system can be applied to any number of suspensions.For example, to estimate characteristics of the four suspensions of avehicle equipped with four wheels, the system includes four pairs ofaccelerometers, i.e., a pair of accelerometers for measuring thevertical accelerations of the wheel and of the body associated with eachsuspension in the above-described manner. The system then determines thecharacteristics of this suspension as a function of the measurementssupplied by this pair of accelerometers in the above-described manner.

1. System for estimating at least one characteristic of at least onemotor vehicle suspension, the or each suspension connecting a wheel ofthe motor vehicle to the body of this vehicle, comprising means foracquiring the vertical accelerations of the wheel and of the body in areferential of the vehicle and means for calculating the at least onecharacteristic of the suspension as a function of the acquired verticalaccelerations of the wheel and of the body.
 2. System according to claim1, wherein each of the at least one characteristic is selected from thegroup consisting of the clearance of the suspension, the clearancevariation speed of the suspension, the coefficient of stiffness of thesuspension, the damping coefficient of the suspension, the spring forceof the suspension, and the damping force of the suspension.
 3. Systemaccording to claim 1, wherein the means for calculating the at least onecharacteristic are adapted to calculate this at least one characteristicbased on a mono-wheel mechanical model of the wheel connected to thebody thereof by means of the suspension.
 4. System according to claim 3,wherein the calculation means comprise means forming Kalman estimatoradapted to estimate the at least one characteristic from the mono-wheelmechanical model.
 5. System according to claim 4, wherein the meansforming Kalman estimator are adapted to implement an extended Kalmanestimator of the state vector${\left( {z_{1}\mspace{14mu} z_{2}\mspace{14mu} z_{3}\mspace{14mu} z_{4}} \right)^{T} = \left( {{deb}\mspace{14mu} {Vdeb}\mspace{14mu} \frac{K_{c}}{m_{c}}\mspace{14mu} \frac{R_{c}}{m_{c}}} \right)^{T}},$where z_(i), i=1, . . . 4, is a state variable, deb is the clearance,Vdeb is the clearance variation speed, m_(c) is the mass of the vehiclebody adjusted to the wheel, K_(c) is the coefficient of stiffness of thesuspension, and R_(c) is the damping coefficient of the suspension. 6.System according to claim 4, wherein the means forming Kalman estimatorare adapted to estimate the state vector (x₁x₂)^(T)=(deb Vdeb)^(T),where deb is the clearance of the suspension and Vdeb is the clearancevariation speed of the suspension.
 7. System according to claim 1,further comprising means for acquiring longitudinal and lateralaccelerations of the body, and in that the means for calculating the atleast one characteristic are adapted to calculate this at least onecharacteristic based on a mono-wheel mechanical model of the wheeltaking into account load transfers in the area of the wheel.
 8. Systemaccording to claim 1, wherein the means for acquiring verticalaccelerations of the wheel and of the body comprise an accelerometerarranged in the body in vertical alignment with the wheel.
 9. Systemaccording to claim 1, wherein the vehicle is equipped with foursuspensions connecting four wheels to the body of this vehicle, and itcomprises, associated with each group composed of a suspensionconnecting a wheel to the body of the vehicle, accelerometers to measurethe vertical accelerations of the wheel and of the body.
 10. Method ofestimating at least one characteristic of a motor vehicle suspension,the or each suspension connecting a motor vehicle wheel to the body ofthis vehicle, comprising a step of acquiring the vertical accelerationsof the wheel and of the body in a referential of the vehicle, and a stepof calculating the at least one characteristic of the suspension as afunction of the acquired vertical accelerations of the wheel and of thebody.
 11. Method according to claim 10, wherein each of the at least onecharacteristic is selected from the group consisting of the clearance ofthe suspension, the clearance variation speed of the suspension, thecoefficient of stiffness of the suspension, the damping coefficient ofthe suspension, the spring force of the suspension, and the dampingforce of the suspension.
 12. Method according to claim 10, wherein thestep of calculating the at least one characteristic comprise calculatingthis at least one characteristic based on a mono-wheel mechanical modelof the wheel connected to the body thereof by means of the suspension.13. Method according to claim 12, wherein the calculation step comprisesusing a Kalman estimator to estimate the at least one characteristicfrom the mono-wheel mechanical model.
 14. Method according to claim 13,wherein the Kalman estimator implements an extended Kalman estimator ofthe state vector${\left( {z_{1}\mspace{14mu} z_{2}\mspace{14mu} z_{3}\mspace{14mu} z_{4}} \right)^{T} = \left( {{deb}\mspace{14mu} {Vdeb}\mspace{14mu} \frac{K_{c}}{m_{c}}\mspace{14mu} \frac{R_{c}}{m_{c}}} \right)^{T}},$where z_(i)i=1, . . . 4, is a state variable, deb is the clearance, Vdebis the clearance variation speed, m_(c) is the mass of the vehicle bodyadjusted to the wheel, K_(c) is the coefficient of stiffness of thesuspension, and R_(c) is the damping coefficient of the suspension. 15.Method according to claim 13, wherein the Kalman estimator estimates thestate vector (x₁x₂)^(T)=(deb Vdeb)^(T), where deb is the clearance ofthe suspension and Vdeb is the clearance variation speed of thesuspension.
 16. Method according to claim 10, further comprising a stepof acquiring longitudinal and lateral accelerations of the body, andwhich the step of calculating the at least one characteristic comprisescalculate this at least one characteristic based on a mono-wheelmechanical model of the wheel taking into account load transfers in thearea of the wheel.
 17. Method according to claim 10, wherein the step ofacquiring vertical accelerations of the wheel and of the body compriseusing an accelerometer arranged in the body in vertical alignment withthe wheel.
 18. Method according to claim 10, wherein the vehicle isequipped with four suspensions connecting four wheels to the body ofthis vehicle, and it comprises, associated with each group composed of asuspension connecting a wheel to the body of the vehicle, accelerometersto measure the vertical accelerations of the wheel and of the body.